Because you cleaned out all traces of Adobe CC you have to start from scratch (that was, by the way, bad advice - all you had to do was OK the install in Security & Privacy). And, some of the Adobe CC apps have 32-bit installers, even though the apps themselves are indeed 64-bit. Hence, you can download the apps individually from Adobe and install most of them, but not all. I don't know about the CC handler program itself... Some of these issues are solved by turning off GateKeeper.
I specifically am not starting on a clean install of Catalina, even though I really really want to. There are just too many applications that are still not 64-bit, or even working with Catalina, and some of these actually work, though you can't install them from scratch.